It seems as though there is a discrepancy between the available information and the current release. Another possibility that I'm considering is that there is a discrepancy between the latest development HEAD and the version bundled with Emacs.

I believe that older versions had an auto-completion popup built-in as something called "senator" which is where the "-menu" functions came from; this would also explain why the popup screenshots I've found are both old and have a distinctly different visual style. The old menu functionality from what I can tell has been removed and that the recommended method is to combine CEDET with auto-complete, which is what I'm doing.

The information is provided by semantic-ia-complete-symbol (thanks djangoliv) but semantic-ia-complete-symbol-menu, part of senator, is no more. So the question now is how to get this information linked in with auto-complete.

I've updated my question. semantic-ia-complete-symbol-menu is not available and seems to be part of senator whose functionality has been replaced by auto-complete. I don't know how to link the two bits together to get the detailed output though.
– ZhroAug 7 '15 at 0:08

Also of note is that completion seems to be borked with semantic-ia-complete-symbol. For example, I perform a completion for rect. of type Rectangle and select int area (void). CEDET then completes it literally with: rect.int area (void)?
– ZhroAug 7 '15 at 0:19

My Emacs does come with an ia.elc in the semantic directory and imports 'semantic/ia just fine. But there is still no semantic-ia-complete-symbol-menu. I'm going to try pulling the latest CEDET from the repo and see if that's any different.
– ZhroAug 7 '15 at 9:25

That was it. semantic-ia-complete-symbol-menu isn't included with Emacs and requires CEDET to be pulled from the repo. Thanks. :)
– ZhroAug 7 '15 at 9:29